Heredia, Maria-Belen

A generic Bayesian approach for the calibration of advanced snow avalanche models with application to real-time risk assessment conditional to snow conditions

Doctorante WP3

Real snow avalanche flows are complex phenomena because of the changing nature of the fluid involved, and, more broadly, the highly nonlinear nature of snow avalanche activity response to snow and weather drivers. Our understanding of the processes at play still increases, however all existing avalanche models, even the most advanced ones, still rely on ad-hoc formulations to a certain degree. ?Hence, for basic understanding, model comparison and validation, and risk assessment improvement, an effort to better relate, on sound mathematical basis, increasingly comprehensive datasets to increasingly advanced models appears as an urgent need.

To this end, the probability of the data can be maximised with respect to the model’s parameters. Asymptotic likelihood theory provides standard errors approximately normally distributed and confidence intervals, which can be used in hypotheses testing and probabilistic forecasts. Bayesian statistics is an alternative avenue of thought, leading credible intervals, the Bayesian counterpart for confidence intervals, but using the posterior pdf instead of the likelihood function, and providing a fair (non-asymptotic) quantification of the actual state of knowledge given data, prior and modelling assumptions. For most models, both Bayesian and Frequentist analyses lead asymptotically to the same inferential results. Besides, uninformative priors can be used to let the data speak for themselves. These two arguments have more or less closed the debate, with Bayesian statistics now been generally accepted as a reasonable option in environmental and social sciences.

From a more practical point of view, the question of how to compute the normalising constant in Bayes theorem has long limited Bayesian analysis to toy models, for which the posterior was explicitly obtainable using conjugate distributions. Nowadays, several algorithms are well suited to overcome the computational difficulties and, among these, Markov Chain Monte Carlo (MCMC) methods are the most popular. In practice, writing MCMC algorithms that converge reasonably quickly needs some practical skill in addition to theoretical knowledge. On the other hand, MCMC methods allow overcoming the inferential challenge, even with highly complex numerical simulation codes, notably using “tricks” like data-augmentation techniques. Additional tools are available within the same framework, providing a complete framework to model selection, model checking and hypothesis testing. Also, link to decision theory is direct, which is appreciable for risk problems.

After deterministic inversion methods had shown their limits, the Bayesian framework has started to be considered as an appealing alternative to model calibration in snow science. Yet, existing implementations have to date generally remained limited to rather simple avalanche models and coarse field data (e.g., samples of runout distances supplemented by input conditions). And when more comprehensive data sets have been considered, improper likelihood formulations have been used. Regarding snow conditions, whereas empirical links could be documented using large data sets, their weakness and the scarcity of the calibration method used make real time avalanche dynamics forecasting conditional to snow conditions still out of reach.

The aim of this PhD is to expand these first efforts by proposing a comprehensive generic Bayesian framework for the calibration of avalanche models and to evaluate the potential of the proposed framework for real-time risk assessment conditional to snow conditions. The proposed approach will be potentially able to work with any kind of avalanche model, and with field data of various complexities (size of the data set, number of variables, as function of the existing measurement devices, etc.).